The end client is the organisation that ultimately receives the contractor's services, the business the work is actually done for. In an off-payroll (Chapter 10) chain it is the party at the top, above any agency, and its size and conduct determine how IR35 operates for the engagement.
The end client's size decides which regime applies. If the client is small under the small company exemption (or wholly overseas with no UK connection), Chapter 10 does not apply and the PSC remains responsible under Chapter 8. If the client is medium or large, Chapter 10 applies and the client takes on the determination duty.
Under Chapter 10 the end client must issue a Status Determination Statement with reasonable care and pass it down the chain. If it fails on either count, the deemed-employer liability falls on the client rather than the fee-payer. The client also operates the client-led disagreement process where a worker challenges a determination. So while the contractor does the work, under Chapter 10 it is the end client, not the contractor, who is in the driving seat on status.